Usenet Newsgroups : rec.puzzles Hall of Fame

The rec.puzzles Hall of Fame is a compilation of over 500 of the most popular puzzles that have been posted and discussed in the rec.puzzles newsgroup. In most cases a detailed solution has been provided.

Newcomb's Problem
A being put one thousand dollars in box A and either zero or one million
dollars in box B and presents you with two choices:
(1) Open box B only.
(2) Open both box A and B.
The being put money in box B only if it predicted you will choose option (1).
The being put nothing in box B if it predicted you will do anything other than
choose option (1) (including choosing option (2), flipping a coin, etc.).
Assuming that you have never known the being to be wrong in predicting your
actions, which option should you choose to maximize the amount of money you
get?